On the locus of higher order jets of entire curves in complex projective varieties

Jean-Pierre Demailly (1)

1 IF - Institut Fourier

For a given complex projective variety, the existence of entire curves is strongly constrained by the positivity properties of the cotangent bundle. The Green-Griffiths-Lang conjecture stipulates that entire curves drawn on a variety of general type should all be contained in a proper algebraic subvariety. We present here new results on the existence of differential equations that strongly restrain the locus of entire curves in the general context of foliated or directed varieties, under appropriate positivity conditions.

Mots clés: projective variety; directed variety; entire curve; jet differential; Green-Griffiths bundle; Semple bundle; exceptional locus; algebraic differential operator; holomorphic Morse inequalities.

Domaines: Géométrie algébrique [math.AG]

Jean-Pierre Demailly. On the locus of higher order jets of entire curves in complex projective varieties. 2021. ⟨hal-03258133⟩